linsolve cannot provide what you want because 
where λ is an eigenvalue becomes singular.
where λ is an eigenvalue becomes singular.Instead, you need to think of how to get the nullspace of 
. In MATLAB, you can use the function null.
. In MATLAB, you can use the function null.A=[2 -2i;2i 5]; % A
lambdaA = round(eig(A)); % Finds values of A
% Note that "rational" option is used otherwise SVD is used in the
% calculation.
v1 = null(A - lambdaA(1) * eye(2), "rational");
v2 = null(A - lambdaA(2) * eye(2), "rational");
v1 = v1 ./ norm(v1, 2)
v2 = v2 ./ norm(v2, 2)
